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3 years ago

9

What is the graph of y-3=-2/3(x+6)?

2 answers:

andreev551 [17]3 years ago

8 0

Answer: First graph is correct.

Step-by-step explanation:

Since we have given that

$y-3=\frac{-2}{3}(x+6)$

For this curve, we can interpretate that

slope of this line is $\frac{-2}{3}$

coordinates of this line = (-6,3).

Since it is in the form of "Two point slope form":

$y-y_0=m(x-x_0)$

Hence, First graph is correct.

jeka57 [31]3 years ago

4 0

The equation has a slope of -2/3 and a Y-intercept of -1.
So the first graph should be your answer

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I need help with my math homework. The questions is: Find all solutions of the equation in the interval [0,2π).

Aleksandr-060686 [28]

Answer:

$\frac{7\pi}{24}$ and $\frac{31\pi}{24}$

Step-by-step explanation:

$\sqrt{3} \tan(x-\frac{\pi}{8})-1=0$

Let's first isolate the trig function.

Add 1 one on both sides:

$\sqrt{3} \tan(x-\frac{\pi}{8})=1$

Divide both sides by $\sqrt{3}$ :

$\tan(x-\frac{\pi}{8})=\frac{1}{\sqrt{3}}$

Now recall $\tan(u)=\frac{\sin(u)}{\cos(u)}$ .

$\frac{1}{\sqrt{3}}=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}$

or

$\frac{1}{\sqrt{3}}=\frac{-\frac{1}{2}}{-\frac{\sqrt{3}}{2}}$

The first ratio I have can be found using $\frac{\pi}{6}$ in the first rotation of the unit circle.

The second ratio I have can be found using $\frac{7\pi}{6}$ you can see this is on the same line as the $\frac{\pi}{6}$ so you could write $\frac{7\pi}{6}$ as $\frac{\pi}{6}+\pi$ .

So this means the following:

$\tan(x-\frac{\pi}{8})=\frac{1}{\sqrt{3}}$

is true when $x-\frac{\pi}{8}=\frac{\pi}{6}+n \pi$

where $n$ is integer.

Integers are the set containing {..,-3,-2,-1,0,1,2,3,...}.

So now we have a linear equation to solve:

$x-\frac{\pi}{8}=\frac{\pi}{6}+n \pi$

Add $\frac{\pi}{8}$ on both sides:

$x=\frac{\pi}{6}+\frac{\pi}{8}+n \pi$

Find common denominator between the first two terms on the right.

That is 24.

$x=\frac{4\pi}{24}+\frac{3\pi}{24}+n \pi$

$x=\frac{7\pi}{24}+n \pi$ (So this is for all the solutions.)

Now I just notice that it said find all the solutions in the interval $[0,2\pi)$ .

So if $\sqrt{3} \tan(x-\frac{\pi}{8})-1=0$ and we let $u=x-\frac{\pi}{8}$ , then solving for $x$ gives us:

$u+\frac{\pi}{8}=x$ ( I just added $\frac{\pi}{8}$ on both sides.)

So recall $0\le x$ .

Then $0 \le u+\frac{\pi}{8}$ .

Subtract $\frac{\pi}{8}$ on both sides:

$-\frac{\pi}{8}\le u$

Simplify:

$-\frac{\pi}{8}\le u$

$-\frac{\pi}{8}\le u$

So we want to find solutions to:

$\tan(u)=\frac{1}{\sqrt{3}}$ with the condition:

$-\frac{\pi}{8}\le u$

That's just at $\frac{\pi}{6}$ and $\frac{7\pi}{6}$

So now adding $\frac{\pi}{8}$ to both gives us the solutions to:

$\tan(x-\frac{\pi}{8})=\frac{1}{\sqrt{3}}$ in the interval:

$0\le x$ .

The solutions we are looking for are:

$\frac{\pi}{6}+\frac{\pi}{8}$ and $\frac{7\pi}{6}+\frac{\pi}{8}$

Let's simplifying:

$(\frac{1}{6}+\frac{1}{8})\pi$ and $(\frac{7}{6}+\frac{1}{8})\pi$

$\frac{7}{24}\pi$ and $\frac{31}{24}\pi$

$\frac{7\pi}{24}$ and $\frac{31\pi}{24}$

5 0

3 years ago

Questions 2,4,5,6,7 and 8 I need help on. I’ll give brainliest to whoever can answer correctly

lions [1.4K]

Answer:

7.

x=16

arc DE=167

arc EF=13

arc DFG=347

3 0

2 years ago

What are the key characteristics of 2d figures?

Dafna1 [17]

Flat and idk the other one

3 0

3 years ago

Isaac goes to an amusement park where tickets for the rides cost $10 per sheet and tickets for the shows cost $15 each.

Digiron [165]

Yeah the tickets is over-priced. Sure the question is not missing ?

7 0

3 years ago

Read 2 more answers

What is this? Please answer with an explanation

Dima020 [189]

Answer:

Slope = -2

Step-by-step explanation:

Since, slope = $\frac{\text{Rise}}{\text{Run}}$

Rise = -(y-intercept)

Run = (x-intercept)

From the graph attached,

y - intercept = -(4) = -4

x - intercept = 2

Therefore, slope the line given in the graph attached will be,

Slope = $\frac{-4}{2}$ = -2

Slope = -2

4 0

2 years ago